An intentional misspelling and mispronunciation that illustrates the hubris of ever claiming that nothing could possibly go wrong. From the episode of The Simpsons where Itchy and Scratchy Land is described as the place "...where nothing could possiblie go wrong. Oh. That's the first thing that's ever gone wrong." Itchy and Scratchy Land is a takeoff of Jurassic Park, which itself is hubris in theme-park form. Possiblie is used when it is obvious that something probably will go wrong.
I don't need to read the instructions. What could possiblie go wrong?
Used with the same meaning as "possibly", but instead lying about the said facts.
"Welcome to Itchy & Scratchy Land, where nothing can possiblie go wrong."